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 bounded set 有界集(36)界集(36)
 有界集
 If for any bounded set M in E, {Bx:x∈M} F' is relatively weakly compact, then B has a unique bilinear extension , whichis separately weakly continuous. 若对于E中任一个有界集M,{B_x:x∈M} F′为相对弱紧,则B具有唯一的分别弱连续的双线性开拓B:E″×F″→K。 短句来源 There exists a MPM space(E,F,T) in which the E is bounded set.  存在M－PM空间（E，F，T），其E是概率有界集． 短句来源 The strong convergence theorem of Ishikawa iterative sequences to the unique solution of the equation x + Tx = f is proved,where x ∈X,X is uniformly convex and uniformly smooth real Banach space,T : D(T)? 奂X? 邛X is m-accretive operator defined on the closed set D(T) of X and its range is a bounded set R(T) of X. 设X是一致凸且一致光滑的实Banach空间,T:D(T),X"X是定义域为闭集D(T),值域为有界集R(T)的m-增生算子,本文证明了Ishikawa迭代强收敛到方程x+Tx=f的唯一解。 短句来源 The results show that this class of equation possesses at least one solution or one positive solution if the "height" of its nonlinear item is appropriate in a bounded set. 结果表明,只要非线性项在某个有界集上的“高度”是适当的,这类方程至少有一个解或者正解. 短句来源 The Borsuk Conjecture has been verified for R3, We give a characterization of Borsuk number of a bounded set in R3, thus completely solve the Borsuk problem in theee dimensional space. 已知Borsuk猜想在R3中是成立的，本文给出R3中有界集Borsuk数的特征，从而完全解决了三维空间中的Borsuk问题． 短句来源 更多
 界集
 If for any bounded set M in E, {Bx:x∈M} F' is relatively weakly compact, then B has a unique bilinear extension , whichis separately weakly continuous. 若对于E中任一个有界集M,{B_x:x∈M} F′为相对弱紧,则B具有唯一的分别弱连续的双线性开拓B:E″×F″→K。 短句来源 There exists a MPM space(E,F,T) in which the E is bounded set.  存在M－PM空间（E，F，T），其E是概率有界集． 短句来源 The strong convergence theorem of Ishikawa iterative sequences to the unique solution of the equation x + Tx = f is proved,where x ∈X,X is uniformly convex and uniformly smooth real Banach space,T : D(T)? 奂X? 邛X is m-accretive operator defined on the closed set D(T) of X and its range is a bounded set R(T) of X. 设X是一致凸且一致光滑的实Banach空间,T:D(T),X"X是定义域为闭集D(T),值域为有界集R(T)的m-增生算子,本文证明了Ishikawa迭代强收敛到方程x+Tx=f的唯一解。 短句来源 The results show that this class of equation possesses at least one solution or one positive solution if the "height" of its nonlinear item is appropriate in a bounded set. 结果表明,只要非线性项在某个有界集上的“高度”是适当的,这类方程至少有一个解或者正解. 短句来源 The Borsuk Conjecture has been verified for R3, We give a characterization of Borsuk number of a bounded set in R3, thus completely solve the Borsuk problem in theee dimensional space. 已知Borsuk猜想在R3中是成立的，本文给出R3中有界集Borsuk数的特征，从而完全解决了三维空间中的Borsuk问题． 短句来源 更多
 “bounded set”译为未确定词的双语例句
 Theorem 3 X is a bornologic space if and only if every uniformly bounded set of linear operators from X to Y is equicontinuous. 定理3 X是囿空间的充要条件为:每个从X到Y的一致有界的线性算子族都是等度连续的. 短句来源 CHARACTERISTICS OF PROBABILISTIC BOUNDED SET ON PN SPACES PN空间中的概率有界性特征 短句来源 The mode transformation function is used to realize the changing between the fuzzy indirect adaptive controller and fuzzy sliding mode controller, which keeps the state of the system changing in a close bounded set. By using Lyapunov method, it is proved that the close-loop system is stable and the tracking errors converge to a neighborhood of zero. 同时利用模式转换函数来实现间接自适应控制与模糊滑模控制之间的转换 ,使系统的状态在有界闭集内变化 ,并依据Lyapunov方法证明了闭环系统稳定 ,跟踪误差收敛到零的一个小邻域内 . 短句来源 Best Simultaneous Approximation of a Uniformly Bounded Set of Real-valued Functions 一致有界实值函数集上的最佳同时逼近 短句来源 This theorem shows that the p-Laplacian can have one positive solution provided the "maximal height" of nonlinear term is appropriate on a bounded set. 这个定理表明此p-L ap lace方程必有一个正解,只要非线性项在某个有界集合上的“最大高度”是适当的. 短句来源 更多

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 bounded set
 We also provide uniform estimates for translates of a bounded set by comparing μn to the associated heat kernel. Sharp rate of average decay of the Fourier transform of a bounded set We consider a functional of the type , where is an open bounded set of and F is a Carathéodory function. Let S be a nonempty bounded set in Rd, d ? 2, and assume that cl S ～ S is a finite union of convex components, each having closure a polytope. Let S be a nonempty bounded set in R2 whose complement consists of a finite number of locally compact components. 更多
 The main aim of this paper is to introduce the conceptions of bounded variation and absolute continuity of an abstract function mapping the close interval [0,1] to the space Λ(μ). The linear space denoted by Λ(μ) in the set of all μ-integrable functions defined on the mesurable set E(μ(E)<+∞).the methods adopted by the author are similar to Mr. Wu. zhon-cing's. He studied the sequence space λ in detail and obtained many results. The main result in this paper may be stated as follows: 1. An abstract function... The main aim of this paper is to introduce the conceptions of bounded variation and absolute continuity of an abstract function mapping the close interval [0,1] to the space Λ(μ). The linear space denoted by Λ(μ) in the set of all μ-integrable functions defined on the mesurable set E(μ(E)<+∞).the methods adopted by the author are similar to Mr. Wu. zhon-cing's. He studied the sequence space λ in detail and obtained many results. The main result in this paper may be stated as follows: 1. An abstract function of bounded variation (abbreviated to BV) or an absolute continous function (abbreviated to AC) is strong BV or strong AC, if it satisfies the the following condition that for any bounded set N(?)Λ~*, U~((N))∈Λ~*. Λ~* is the dual space of Λ and U~((N)): u~((N))(s) =(?)|u(s)|. 2. An abstract function is AC, if and only if, (1) x(s,t) is the AC function in ordinary meaning except at a null set; (2) the total variation (?)(x(s_1,t))∈Λ~(**). 3. The product of two BV functions (or two AC functions) is a BV function (or AC function) if and only if, for any BV function (or AC function) Z(t), Λ_Z~*(?)Λ~*, here, Λ_Z~*={U~Z=u(s)[z(s.0)+(?)(z(s,t))]:U∈Λ~*}.4. If the space Λ is complete, a necessary and sufficient condition for an abstract function X(t) to be the BV function is that X(t) can be decomposed into the difference of two increasing functions. 吴从炘曾经研究了在叙列空间上取值的囿变函数,并取得了许多结果。实际上,一些结果对在叙列空间上取值的绝对连续函也成立。本文主要讨论在Λ(μ)空间上取值的囿变函数,采用的方法相似于[1]中的方法,得到一些相应的结果。同时引入Λ(μ)空间上取值的绝对连续函数,得到一些有关绝对连续函数的结果。此外,李文琦、马绍芹的结果在这里也容易推出。设(X,ψ,μ)是完全测度空间,E∈ψ且μ(E)<+∞,在E上μ一可积的函数所构成的空间记为Λ(μ),一切满足的可测函数U=u(s)的全体叫做空间Λ(μ)的对偶,记作Λ~*(μ)。Λ(μ)与Λ~*(μ)分别简记作Λ、Λ~*。如果Λ=Λ~(**),则称空间Λ是完全的。设X(t)=x(s,t)是从[0,1]到空间Λ的抽象函数,如果对于每个U∈Λ~*,是有界的,则称集合M是有界集。如果对于每个有界集N(?)A~*,是有界的,则称集合是全有界的。设{X_n}是空间Λ上抽象函数的叙列,如果对于一切U∈Λ~*,{UX_n}收敛,则称{X_n}是弱收敛的;如果{UX_n}在对偶空间A~*中每个有界集上一致收敛,则称{X_n}是强收敛的。 In paper(1),a class of geometric inequalities have been constructed on the bounded set of points,and some relations of the invariants for the k-ciimcnsional simplex in the Euclidean space have been given by the algebric methods. The well-known Neuberg-Pcodc inequality concerning two triangles has been extended to any two simplices in the n-dimensional Euclidean space in(2). This paper obtains two inequalities ( Theorem 1 and Theorem 2) concerning any two simplices from another viewpoint. As the special... In paper(1),a class of geometric inequalities have been constructed on the bounded set of points,and some relations of the invariants for the k-ciimcnsional simplex in the Euclidean space have been given by the algebric methods. The well-known Neuberg-Pcodc inequality concerning two triangles has been extended to any two simplices in the n-dimensional Euclidean space in(2). This paper obtains two inequalities ( Theorem 1 and Theorem 2) concerning any two simplices from another viewpoint. As the special cases of these two inequalities,we may deduce some other relations among the invariants,which differ from that in (1) 文章[1]利用代数方法建立了有限点集的一类几何不等式,给出了n维欧氏空间中k(k≤n)维单形的一些不变量的关系式;该文作者又在文[2]中将著名的涉及到两个三角形的Neubery—Peode不等式推广到n维欧氏空间的任意两个单形。本文将从另一角度给出n维欧氏空间中的两个关于两个任意单形的不等式(定理1及定理2),而且作为这两个不等式的特例,可导出另一些不同于文[1]中的不变量之间的关系式。 Ih this paper we introduce idempotently decreasing sequences and i—bounded compact sets such that they provide a set of equivelent propertions about i bounologieal algebra. Further we havr studied the algebra k[x]. It is an i—bornological algebra under the locally m—convex topology J_x. Hence on and algebra E it naturally produces an i—bornological algebra, the intrinsic i—bornological algebra as I call it. In §3, we obtain the condition of an i—bounded set t_0 be a subalgebra (0), and a sufficient condition... Ih this paper we introduce idempotently decreasing sequences and i—bounded compact sets such that they provide a set of equivelent propertions about i bounologieal algebra. Further we havr studied the algebra k[x]. It is an i—bornological algebra under the locally m—convex topology J_x. Hence on and algebra E it naturally produces an i—bornological algebra, the intrinsic i—bornological algebra as I call it. In §3, we obtain the condition of an i—bounded set t_0 be a subalgebra (0), and a sufficient condition for a locally m—convex algebra t_0 be an i—bornolegical algebra on E. 在本文中引进幂等下降列及i—有界紧集之后,可以得到一组关于i—包囿代数的等价性命题。我们讨论了代数K[x],它在局部m—凸拓扑j_x下是i—包囿代数。由此在任意代数E上自然地产生一个i—包囿代数,它称作固有i—包囿代数。在§3中,我们得到了一个i—有界集是{0}子代数的条件以及E上一个局部m—凸代数是i—包囿代数的充分条件, << 更多相关文摘
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